AbstractFunction spaces of generalized smoothness have been introduced and considered from different points of view - characterisation by approximation, interpolation, operators, differences. This have been done by a variety of authors particularly since the middle of the Seventies up to the end of the Eighties. The last years have again witnessed great interest in this question, especially in connection with embeddings and limiting embeddings. We consider here the Fourier-analytical approach for such spaces. This gives, in particular, most of the spaces defined by the methods described above. Furthermore, we derive some consequences for embedding results.